3-Colourability problem

(1,2)-polar
(2,0)-colorable
2-split ∩ perfect
2-threshold
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,K_1,4,X₈₅)-free
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,X₈₅)-free
(2K₂,3K₁)-free
(2K₂,4K₁,C₅,co-diamond)-free
(2K₂,4K₁,co-claw,co-diamond)-free
(2K₂,A,H)-free
(2K₂,C₄)-free
(2K₂,C₅,C₆,C₇,C₈,co-claw,co-diamond)-free
(2K₂,C₅,C₆,net)-free
(2K₂,C₅,T₂)-free
(2K₂,C₅)-free
(2K₂,C₆,odd anti-cycle)-free
(2K₂,P₆)-free
(2K₂,X₉₁,co-claw)-free
(2K₂,claw)-free
(2K₂,co-diamond)-free
(2K₂,house)-free
(2K₂,net)-free
(2K₂,odd anti-hole)-free
2K₂-free
2K₂-free ∩ probe cograph
(2K₃ + e,3K₁,C₅,T₂,X₁₈,X₉₄,co-domino)-free
(2K₃ + e,5-pan,A,C₆,E,K_3,3-e,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₃₇,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,5-pan,A,C₆,E,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₃₇,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,antenna,co-antenna,co-domino,co-fish,co-twin-C₅,co-twin-house,domino,fish,twin-C₅,twin-house)-free
(2K₃ + e,C₅,C₆,P₆,X₅,2P₄,A,C₆,C₇,E,P₇,R,X₁,X₁₀₃,X₅,X₅₈,X₈₄,X₉₈,antenna,co-domino,co-rising sun,co-twin-house,domino,parachute,parapluie,rising sun,sunlet₄)-free
(2K₃,2K₃ + e,3K₁,A,H,T₂,X₁₈,X₄₅,co-domino)-free
(2K₃,2P₃,C₅,C₆,C₇,K_2,3,K₃ ∪ P₃,X₈₄,3K₂,C₄ ∪ P₂,C₆,P₂ ∪ P₄,P₆,X₁₈,X₅,co-antenna,co-domino,co-fish)-free
(2K₃,3K₁,A,H,X₄₅)-free
(2K₃,4K₁,C₇,X₃₈,X₃₉,W₄ ∪ K₁,W₅,X₈₆,X₈₇,X₈₈,X₈₉,X₉₀,butterfly ∪ K₁,diamond)-free
(2P₃,3K₂,C₄ ∪ P₂,C₆,K_2,3,P₆,X₁₃₀,X₁₃₂,X₁₃₄,X₁₅₂,X₁₅₃,X₁₅₄,X₁₅₅,X₁₅₆,X₁₅₇,X₁₅₈,X₁₈,X₈₄,X₁₁,X₁₂₇,X₁₂₈,X₁₂₉,X₁₃₁,X₁₃₃,X₁₃₅,X₁₃₆,X₁₃₇,X₁₃₈,X₁₃₉,X₁₄₀,X₁₄₁,X₁₄₂,X₁₄₃,X₁₄₄,X₁₄₅,X₁₄₆,X₁₄₇,X₁₄₈,X₁₄₉,X₁₅₀,X₁₅₁,X₃₀,X₃₅,X₄₆,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺³,co-antenna,co-eiffeltower,co-longhorn,domino,fish,odd anti-hole)-free
(2P₃,triangle)-free
2P₃-free
(2P₄,A,C₅,C₆,C₇,E,K_3,3-e,P₇,R,X₁,X₁₀₃,X₅,X₅₈,X₈₄,X₉₈,C₆,P₆,X₅,sunlet₄,co-antenna,co-domino,co-rising sun,domino,parachute,parapluie,rising sun,twin-house)-free
(3K₁,C₅,K₃ ∪ K₄,BW₃,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃)-free
(3K₁,C₅,K₅ - e,C₆ ∪ K₁,C₇,K_3,3 ∪ K₁,K_3,3-e ∪ K₁,domino ∪ K₁)-free
(3K₁,C₅,C₆,X₁₆₄,X₁₆₅,sunlet₄)-free
(3K₁,2P₃)-free
(3K₁,3K₂)-free
(3K₁,C₆)-free
(3K₁,E)-free
(3K₁,H)-free
(3K₁,K_1,5)-free
(3K₁,K₂ ∪ claw)-free
(3K₁,P₂ ∪ P₄)-free
(3K₁,P₆)-free
(3K₁,T₂,X₂,X₃,anti-hole)-free
(3K₁,X₁₇₂)-free
(3K₁,co-cross)-free
3K₁-free
(3K₂,A,C₄ ∪ 2K₁,E,P₂ ∪ P₃,R,K₅ - e,co-claw,net,odd anti-hole,twin-house)-free
(3K₂,C₄ ∪ P₂,C₅,C₆,K₂ ∪ K₃,K_3,3,K_3,3+e,P₂ ∪ P₄,P₆,X₁₈,X₅,2P₃,C₆,C₇,X₈₄,antenna,domino,fish)-free
(3K₂,C₅,C₇,P₂ ∪ P₄,X₁₇₃,X₁₁,net)-free
(3K₂,C₅,P₂ ∪ P₄,net)-free
(3K₂,E,P₂ ∪ P₄,net,odd anti-hole,odd-hole)-free
(3K₂,E,P₂ ∪ P₄,net)-free
(3K₂,P,co-gem,house)-free
(3K₂,co-paw,odd anti-hole)-free
(3K₂,triangle)-free
(3P₃,P₃ ∪ P₄,P₅,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,X₁₈₄,X₁₈₅,X₁₈₆,X₁₈₇,X₁₈₈,X₁₈₉,X₁₉₀,X₁₉₁,X₁₉₂,X₁₉₃,5-pan,A,P₆,co-twin-C₅)-free
(4K₁,C₇,S₃,X₁₇₅,X₁₇₆,X₄₂,X₃₆,claw,co-antenna,net,odd anti-hole)-free
(4K₁,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,house)-free
(4K₁,C_n+4)-free
(4K₁,co-claw,co-diamond)-free
(4K₁,house)-free
(4K₁,net)-free
(4K₁,odd anti-hole,odd-hole)-free
4K₁-free
(5,2)-chordal
(5,2)-odd-chordal
(5,2)-odd-crossing-chordal
(5,2)-odd-noncrossing-chordal
(5-pan,A,P₆,X₁₈₆,3P₃,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,X₁₈₄,X₁₈₅,X₁₈₇,X₁₈₈,X₁₈₉,X₁₉₀,X₁₉₁,X₁₉₂,X₁₉₃,house,twin-C₅)-free
(6-fan,C₄ ∪ P₂,C₅,C₆ ∪ K₁,C₇,K₂ ∪ K₃,K_2,3,P₂ ∪ P₄,W₄ ∪ K₁,W₆,X₁₃₂,X₁₆₉,X₁₇₆,X₁₈,X₁₉₇,X₁₉₈,X₁₉₉,X₂₀₀,X₂₀₁,X₂₀₂,X₃₅,X₈₄,C₄ ∪ P₂,C₆ ∪ K₁,C₇,P₂ ∪ P₄,W₄ ∪ K₁,W₆,X₁₃₂,X₁₆₉,X₁₇₆,X₁₈,X₁₉₇,X₁₉₈,X₁₉₉,X₂₀₀,X₂₀₁,X₃₅,X₈₄,butterfly ∪ K₁,butterfly ∪ K₁,co-6-fan,co-fish,fish)-free
(A ∪ K₁,K_1,4,W₄,W₅,co-4-fan,co-fork ∪ K₁,gem ∪ K₁,net ∪ K₁)-free
(A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,K₅ - e,W₅,co-claw,twin-C₅,twin-house)-free
(A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,K₅ - e,co-claw,odd anti-hole,twin-house)-free
(A,C₅,C₆,P₆,domino,house)-free
(A,E,S₃,X₁,domino,hole,house,net,rising sun)-free
(A,P₆,clique wheel,domino,hole,house)-free
(A,P₆,domino)-free
AT-free
AT-free ∩ claw-free
Berge
Berge ∩ bull-free
Berge ∩ claw-free
(C₄,P₅)-free
(C₄,P₆)-free
(C₄,odd-hole)-free
(C₅,C₆,C₇,C₈,P₈,X₁₉,X₂₀,X₂₁,X₂₂,gem,house)-free
(C₅,C₆,P₆,C₆,P₆,X₁₇,X₁₈,X₅,X₉₈,co-antenna,co-domino)-free
(C₅,C₆,P₆,C₆,P₆)-free
(C₅,P,P₅,P,bull,co-gem,fork)-free
(C₅,P₂ ∪ P₃,house)-free
(C₅,P₅,A,C₆,P₆,co-domino)-free
(C₅,P₅,C₆,C₇,C₈,P₈,X₁₉,X₂₀,X₂₁,X₂₂,co-gem)-free
(C₅,P₅,P,co-fork,co-gem,fork)-free
(C₅,P₅,P₂ ∪ P₃)-free
(C₅,P₅,gem)-free
(C₅,P₅)-free
(C₅,P₆,P₆)-free
(C₅,S₃,X₁₁,3K₂,C₇,P₂ ∪ P₄,X₁₇₃)-free ∩ co-line
(C₅,bull,co-gem,gem)-free
(C₅,co-gem,gem)-free
(C₅,co-gem,house)-free
(C₆,K₂ ∪ K₃,X₁₀₃,X₃₇,X₈₈,X₉₀,C_n+4 ∪ K₁,T₂,net ∪ K₁,co-diamond,co-domino,co-eiffeltower,co-twin-C₅)-free
(C₆,P₆,P₆,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₅,X₆,X₇,X₈,X₉,anti-hole,co-antenna)-free
(C₆,C₆)-free murky
(C_n+4 ∪ K₁,C(n,k),W₄,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4 ∪ K₁,C(n,k),X₄₂,T₂,X₂,X₃,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4 ∪ K₁,K_2,3,T₂,C₆,X₁₀₃,X₃₇,X₈₈,X₉₀,diamond,domino,eiffeltower,net ∪ K₁,twin-C₅)-free
(C_n+4 ∪ K₁,K_2,3,T₂,X₉₀,domino,paw,twin-C₅)-free
(C_n+4 ∪ K₁,S₃ ∪ K₁,X₄₂,T₂,X₂,X₃,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4 ∪ K₁,S₃,W₄,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,X₃₇,X₃₈,X₃₉,X₄₀,X₄₁,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,co-XF₁²ⁿ⁺³,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²,odd anti-hole)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,XF₁²ⁿ⁺³,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,co-XF₁²ⁿ⁺³,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²,odd anti-hole)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,XF₁²ⁿ⁺³,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,co-XF₁²ⁿ⁺³,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²,odd-hole)-free
(C_n+6,X₃₇,claw,co-antenna,net,sun)-free
D
Dilworth 3
Dilworth 4
Gallai
Gallai-perfect
(H,K₃ ∪ 2K₁,C_n+4,K₅ - e,X₁₀₀,X₁₀₁,X₁₀₂,co-4-fan,net)-free
(H,K₃ ∪ 2K₁,C_n+4,K₅ - e,co-4-fan,net)-free
HH-free
HHD-free
HHDA-free
HHDS-free
HHG-free
HHP-free
Helly circle
Helly circular arc
Helly circular arc ∩ self-clique
(K_1,4,P,P₅,fork)-free
(K_1,4,P₅)-free
(K_1,4,paw)-free
(K₂ ∪ K₃,P₅,X₃₇,X₃₈,co-diamond,co-domino,co-twin-C₅)-free
(K₂ ∪ K₃,X₁₁,X₁₂₇,X₁₂₈,X₁₂₉,X₁₃₁,X₁₃₃,X₁₃₅,X₁₃₆,X₁₃₇,X₁₃₈,X₁₃₉,X₁₄₀,X₁₄₁,X₁₄₂,X₁₄₃,X₁₄₄,X₁₄₅,X₁₄₆,X₁₄₇,X₁₄₈,X₁₄₉,X₁₅₀,X₁₅₁,X₃₀,X₃₅,X₄₆,XF₁²ⁿ⁺³,XF₆²ⁿ⁺³,2P₃,3K₂,C₄ ∪ P₂,C₆,P₆,X₁₃₀,X₁₃₂,X₁₃₄,X₁₅₂,X₁₅₃,X₁₅₄,X₁₅₅,X₁₅₆,X₁₅₇,X₁₅₈,X₁₈,X₈₄,antenna,co-domino,co-fish,eiffeltower,longhorn,odd-hole)-free
(K₂ ∪ K₃,X₉₀,C_n+4 ∪ K₁,T₂,co-domino,co-paw,co-twin-C₅)-free
(K₂ ∪ K₃,co-diamond)-free
(K₂ ∪ claw,triangle)-free
(K_2,3,P,P₅)-free
(K_2,3,P₅)-free
(K_3,3,3,C_n+4)-free
(K_3,3,K_3,3+e,2P₃,C_n+4)-free
(K_3,3,P₅)-free
(K_3,3,C_n+4)-free
(K_3,3-e,P₅,X₉₈)-free
(K_3,3-e,P₅,X₉₉)-free
(K_3,3-e,P₅)-free
(K_4,4,P₅)-free
(K₄,P₅)-free
(K₅ - e,S₃,3K₂,A,C₄ ∪ 2K₁,E,P₂ ∪ P₃,R,claw,co-twin-house,odd-hole)-free
(K₅ - e,A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,claw,co-twin-house,odd-hole)-free
Meyniel
Meyniel ∩ weakly chordal
N^*
N^*-perfect
(P,P₅,3K₂,gem)-free
(P,P₅,co-fork)-free
(P,P₅)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-gem,house)-free
(P₂ ∪ P₃,house)-free
(P₂ ∪ P₄,triangle)-free
P₂ ∪ P₄-free
P₄-brittle
P₄-comparability
P₄-indifference
P₄-simplicial
(P₅,S₃,A,E,X₁,anti-hole,co-domino,co-rising sun,net)-free
(P₅,X₈₂,X₈₃)-free
(P₅,A,P₆,anti clique wheel,anti-hole,co-domino)-free
(P₅,A,anti-hole,co-domino)-free
(P₅,C₆)-free
(P₅,C₆)-free ∩ weakly chordal
(P₅,P,anti-hole)-free
(P₅,P,gem)-free
(P₅,P₂ ∪ P₃)-free
(P₅,X₃₈,co-gem)-free
(P₅,anti-hole,co-bicycle,co-domino)-free
(P₅,anti-hole,co-domino,co-gem)-free
(P₅,anti-hole,co-domino,co-sun)-free
(P₅,anti-hole,co-domino)-free
(P₅,anti-hole,co-gem)-free
(P₅,anti-hole)-free
(P₅,bull,co-fork)-free
(P₅,bull,odd anti-hole)-free
(P₅,bull)-free
(P₅,claw)-free
(P₅,co-domino,co-gem)-free
(P₅,co-fork)-free
(P₅,cricket)-free
(P₅,fork)-free
(P₅,gem)-free
(P₅,house)-free
P₅-free
P₅-free ∩ weakly chordal
(P₆,X₃₀,X₈)-free
(P₆,triangle)-free
P₆-free
PI
PI^*
(S₃,T₂,X₂,X₃,C_n+4 ∪ K₁,C(n,k),X₄₂,even-hole,odd-cycle ∪ K₁)-free
(S₃,T₂,X₂,X₃,C_n+4 ∪ K₁,S₃ ∪ K₁,X₄₂,even-hole,odd-cycle ∪ K₁)-free
(S₃,3K₂,E,P₂ ∪ P₄,odd anti-hole,odd-hole)-free
(S₃,3K₂,E,odd-hole)-free ∩ line
(S₃,C_n+4 ∪ K₁,C(n,k),W₄,even-hole,odd-cycle ∪ K₁)-free
(S₃,C_n+4 ∪ K₁,W₄,even-hole,net,odd-cycle ∪ K₁)-free
(S₃,C_n+4,S₃ ∪ K₁,co-claw)-free
(S₃,C_n+4,T₂)-free
(S₃,C_n+4,co-claw,net)-free
(S₃,C_n+4,co-claw)-free
(S₃,C_n+4,net)-free
(T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,anti-hole,co-XF₁²ⁿ⁺³,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²,hole)-free
(W₄,claw,gem,odd-hole)-free
(W₄,gem)-free ∩ short-chorded
Welsh-Powell opposition
(X₁₀₃,C_n+4,S₃ ∪ K₁,net ∪ K₁,co-claw,co-eiffeltower)-free
(X₁₂,X₅,X₉₅,X₉₆,X₉₇,X₁₂,X₅,X₉₅,X₉₆,X₉₇,claw ∪ triangle,claw ∪ triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free
(X₁₇₂,triangle)-free
(X₃₄,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,C_n+4,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
(X₃₇,diamond,even-cycle)-free
(XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₇,XC₈)-free
(XC₇,XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₈)-free
(XF₁²ⁿ⁺³,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,odd-hole)-free
(XF₁²ⁿ⁺³,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,anti-hole,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,hole)-free
β-perfect
β-perfect ∩ co-β-perfect
(G)-perfect
(3K₂,C₆,P₇,X₁₆₄,X₁₆₅,sunlet₄,odd anti-cycle)-free
(A,T₂,odd anti-cycle)-free
(C_n+3 ∪ K₁,co-diamond,co-paw)-free
(C_n+4,H)-free
(C_n+4,T₂,X₃₁,co-XF₂ⁿ⁺¹,co-XF₃ⁿ)-free
(C_n+4,T₂,co-XF₂ⁿ⁺¹)-free
(C_n+4,X₅₉,co-longhorn)-free
(C_n+4,bull,co-dart,co-gem)-free
(C_n+4,co-claw,co-gem)-free
(C_n+4,co-claw)-free
(C_n+4,co-diamond)-free
(C_n+4,co-gem)-free
(C_n+4,co-sun)-free
(C_n+4,net)-free
(C_n+4,odd co-sun)-free
C_n+4-free
(C_n+6,odd anti-cycle)-free
(E,odd anti-cycle)-free
(K_1,4,co-diamond)-free
(K_1,4,co-paw)-free
(K_1,4,odd anti-cycle)-free
(P₇,star_1,2,3,sunlet₄,odd anti-cycle)-free
(P₇,star_1,2,3,odd anti-cycle)-free
(T₂,co-cycle)-free
(T₃,X₈₁,co-cycle)-free
(T₃,co-cycle)-free
(W₄,W₅,co-butterfly)-free
(W₄,co-claw,co-gem,odd anti-hole)-free
(W₄,co-claw,co-gem)-free
(W₄,co-claw)-free
(W₄,co-gem)-free
(X₁₇₇,odd anti-cycle)-free
(X₃₇,co-diamond,even anti-cycle)-free
XC₁₀-free
(XC₁₁,co-claw,co-diamond)-free
(XC₁₁,odd anti-cycle)-free
(XC₁₂,co-cycle)-free
XC₁₂-free
(claw ∪ 3K₁,odd anti-cycle)-free
(star_1,2,3,sunlet₄,odd anti-cycle)-free
(star_1,2,3,odd anti-cycle)-free
absolutely perfect
absorbantly perfect
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
(anti-hole,bull,odd-hole)-free
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,co-sun,hole)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
(anti-hole,odd-hole)-free
b-perfect
balanced ∩ co-line
balanced ∩ line
basic perfect
biclique separable
bip^*
bipartable
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipolarizable
bithreshold
bitolerance
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 2 ∩ co-bipartite
brittle
(bull,co-fork,co-gem)-free
(bull,co-gem,gem)-free
(bull,hole,odd anti-hole)-free
(bull,house,odd-hole)-free
(bull,odd anti-hole,odd-hole)-free
bull-free ∩ perfect
charming
chordal ∪ co-chordal
chordal-perfect
circle
circle ∩ diamond-free
circle graph with equator
circular arc
circular arc ∩ clique-Helly
circular arc ∩ co-bipartite
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular perfect
circular permutation
(claw,diamond,odd-hole)-free
(claw,odd anti-hole,odd-hole)-free
claw-free ∩ perfect
clique graphs of Helly circular arc
clique graphs of normal Helly circular arc
clique separable
cliquewidth 3
cliquewidth 4
co-2-subdivision
co-Gallai
co-HHD-free
co-Matula perfect
co-Meyniel
co-P₄-brittle
co-Welsh-Powell opposition
co-Welsh-Powell perfect
co-β-perfect
co-biclique separable
co-bipartite
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold
co-bounded tolerance
co-building-free
(co-butterfly,co-gem)-free
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-claw,odd anti-hole,odd-hole)-free
co-comparability
co-comparability ∩ comparability
co-comparability ∩ tolerance
co-comparability ∪ comparability
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension 2, height 1
co-comparability graphs of posets of interval dimension d
co-cycle-free
(co-diamond,even anti-cycle)-free
(co-diamond,house)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-forest-perfect
(co-gem,gem)-free
(co-gem,house)-free
co-gem-free
co-hereditary clique-Helly
co-interval
co-interval ∪ interval
co-interval bigraph
co-interval containment bigraph
co-line
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
co-paw-free
co-perfectly orderable
co-probe cograph
co-proper interval bigraph
co-strongly chordal
co-tolerance
co-trapezoid
cograph contraction
comparability
comparability ∩ weakly chordal
comparability graphs of dimension 2 posets
comparability graphs of dimension 3 posets
comparability graphs of dimension 4 posets
comparability graphs of dimension d posets
comparability graphs of posets of interval dimension 2
comparability graphs of posets of interval dimension d
comparability graphs of semiorders
concave-round
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex-round
cycle-bicolorable
d-trapezoid
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free ∩ perfect
domination
double-split
doubled
even anti-cycle-free
even-hole-free ∩ probe chordal
extended P₄-laden
forest-perfect
generalized strongly chordal
good
gridline
hereditary N^*-perfect
hereditary clique-Helly ∩ line ∩ perfect
hereditary homogeneously orderable
(hole,odd anti-hole)-free
(house,hole,domino,sun)-free
house-free ∩ weakly chordal
i-triangulated
intersection graphs of parallelograms (squares)
k-polygon
kernel solvable
line ∩ perfect
line graphs of bipartite graphs
line graphs of bipartite multigraphs
locally perfect
module-composed
multitolerance
murky
nK₂-free, fixed n
nP₃-free, fixed n
neighbourhood perfect
normal Helly circular arc
normal circular arc
odd anti-cycle-free
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
opposition
overlap
parallelepiped
parity
path orderable
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect connected-dominant
perfectly 1-transversable
perfectly contractile
perfectly orderable
permutation
preperfect
probe Gallai
probe HHDS-free
probe Meyniel
probe P₄-reducible
probe P₄-sparse
probe chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-trivially perfect
probe cograph
probe distance-hereditary
probe interval
probe ptolemaic
probe split
probe strongly chordal
probe trivially perfect
probe unit interval
proper Helly circular arc
proper circular arc
proper tolerance
pseudo-split
quasi-Meyniel
quasi-brittle
quasi-parity
quasitriangulated
semiperfectly orderable
short-chorded
skeletal
slender
slightly triangulated
slim
split-perfect
strict 2-threshold
strict quasi-parity
strong asteroid free
strong tree-cograph
strongly circular perfect
strongly orderable
strongly perfect
sun-free ∩ weakly chordal
superperfect
threshold tolerance
tolerance
totally unimodular
trapezoepiped
trapezoid
tree-cograph
tree-perfect
unimodular
unit Helly circular arc
unit circular arc
unit tolerance
very strongly perfect
weak bipolarizable
weakly chordal
wing-triangulated

Input:	A graph G in this class.
Output:	True iff each vertex of G can be assigned one colour out of 3 such that whenever two vertices are adjacent, they have different colours.

Problem: 3-Colourability

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI